Archimedes Texts

Here it is to be noted, that the River it self may have sundry
and divers heights, in several parts of its Chanel, by reason of
the various velocities of the water, and its measures; as hath
been demonstrated in the first book.

It is supposed, that the Rivers equal in breadth, and quick
height, that have the same inclination of bed or bottom, ought
also to have equal velocities, the accidental impediments being
removed that are dispersed throughout the course of the water,
and abstracting also from the external windes, which may velo
citate, and retard the course of the water of the River.

Let us suppose also, that if there be two Rivers that are in
their beds of equal length, and of the same inclination, but of
quick heights unequal, they ought to move with like velocity,
according to the sense explained in the second definition.

Because it will often be requisite to measure the time exactly
in the following Problems, we take that to be an excellent
way to measure the time, which was shewed me many years since
by Signore Galilæo Galilæi, which is as followeth.

A string is to be taken three Roman feet long, to the end of
which a Bullet of Lead is to be hanged, of about two or three
ounces; and holding it by the other end, the Plummet is to be
removed from its perpendicularity a Palm, more or less, and then
let go, which will make many swings to and again, passing and
repassing the Perpendicular, before that it stay in the same: Now
it being required to measure the time that is spent in any what
soever operation, those vibrations are to be numbred, that are
made whilst the work lasteth; and they shall be so many second
minutes of an hour, if so be, that the string be three Roman feet
long, but in shorter strings, the vibrations are more frequent, and
in longer, less frequent; and all this still followeth, whether the
Plummet be little or much removed from its Perpendicularity, or
whether the weight of the Lead be greater or lesser.